cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A052496 Number of nonsingular n X n matrices over GF(8).

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%I A052496 #18 Jul 06 2025 02:54:57
%S A052496 1,7,3528,115379712,241909719367680,32467582052437076213760,
%T A052496 278893342293098904613804037898240,
%U A052496 153323163270070838469523866093442017326530560
%N A052496 Number of nonsingular n X n matrices over GF(8).
%H A052496 G. C. Greubel, <a href="/A052496/b052496.txt">Table of n, a(n) for n = 0..30</a>
%F A052496 a(n) = (8^n - 1)*(8^n - 8)*...*(8^n - 8^(n-1)).
%F A052496 a(n) = A109966(n)*A027876(n). - _Bruno Berselli_, Jan 30 2013
%F A052496 a(n) ~ c * 8^(n^2), where c = A132036. - _Amiram Eldar_, Jul 06 2025
%t A052496 Table[Product[(8^n - 8^j), {j, 0, n-1}], {n, 0, 10}] (* _G. C. Greubel_, May 14 2019 *)
%o A052496 (Magma) [1] cat [&*[(8^n-8^k): k in [0..n-1]]: n in [1..10]]; // _Bruno Berselli_, Jan 30 2013
%o A052496 (PARI) {a(n) = prod(j=0,n-1, 8^n - 8^j)}; \\ _G. C. Greubel_, May 14 2019
%o A052496 (Sage) [product(8^n - 8^j for j in (0..n-1)) for n in (0..10)] # _G. C. Greubel_, May 14 2019
%Y A052496 Cf. A027876, A109966.
%Y A052496 Cf. A002884, A003791, A053290, A053291, A053292, A053293, A052497, A052498, A132036.
%K A052496 easy,nonn
%O A052496 0,2
%A A052496 _Vladeta Jovovic_, Mar 16 2000